While a useful memory jogger for some, I've found that "low to high, clear the sky/high to low, look out below" etc. tends to be confusing for many people.
I've had success having learners visualize how the "legacy" instrument works. The altimeter really just measures atmospheric pressure and presents it as an altitude. The altimeter itself is sealed, connected via plumbing to a static port. There's a little aneroid inside which expands or contracts based on changes in pressure. If pressure drops inside the chamber, the aneroid expands. If the pressure becomes greater, it contracts. As it does so, gears rotate the hands of the display to indicate altitude. That's it!
At the dawn of aviation, altimeters couldn't be quickly and easily calibrated for changing barometric pressures, which was a real problem. So in 1936 Paul Kollsman invented a way to do that. The sensitive altimeter was born and to this day pilots use the "Kollsman window" to set their altimeters to local pressure, in measurements of hectopascals or inches of mercury.
With that in mind, here's an artificial scenario: freeze frame an airplane in flight. Local pressure is 29.92". Altimeter indicates 2,000 feet.
Let's use our global weather control panel to lower the local pressure from 29.92" to 29.82" with that airplane still frozen in flight.
Inside the airplane, within the sealed chamber of the altimeter itself, pressure dropped by a tenth of an inch of mercury. As a result, the aneroid expanded. The gears turned. The indicated altitude increased by 100 feet.
If we unfreeze the frame and let the airplane fly, the pilot suddenly sees 2,100 feet indicated on the altimeter. There are two ways to make the instrument indicate the desired altitude, 2,000 feet again. Option a) is to obtain a local pressure setting. The pilot rotates the knob so that the Kollsman window indicates 29.82" instead of 29.92". Voila. Now the altimeter indicates 2,000 feet on the nose again. Option b) is to descend 100 feet. Of course doing so would result in the aircraft's true altitude being 1,900 feet even though the altimeter itself indicates 2,000.
Since not all pilots choose option a), this is where "high to low, look out below" comes from.